xf = xi + vxit + 1/2axt²
position as a function of time
The equation you posted is commonly known as the displacement formula in physics. It describes the displacement of an object given its initial position, velocity, acceleration, and time. Here is a breakdown of the terms in the equation:
– xf: represents the final position of the object.
– xi: represents the initial position of the object.
– vx: represents the horizontal component of the velocity of the object.
– t: represents the time elapsed since the object started moving.
– ax: represents the horizontal component of the acceleration of the object.
The formula can be derived from the more general equation for displacement, which is:
x = x0 + vt + 1/2at^2
where x0 is the initial position (equivalent to xi) and v and a are the velocity and acceleration vectors respectively. When we only consider the horizontal component of velocity and acceleration, we get the formula you posted.
It’s worth noting that this formula assumes constant acceleration, which means that ax and any other horizontal components of acceleration remain constant throughout the motion. Additionally, it only applies to motion in one dimension (i.e., horizontally). In more complex situations with motion in multiple directions or changing acceleration, the formula would need to be modified accordingly.
More Answers:
The Derivative: Calculating Instantaneous Rates Of Change In MathThe Relationship Between Velocity And Acceleration: Derivative Calculation Explained.
Kinematics: Solving For Final Velocity Using The Vxf² = Vxi² + 2Ax(∆X) Equation